Cumulenes are a class of compounds with C=C chains directly connected ( like ...=C=C=C=C=...).
I can't assume that you are necessarily talking about a particular cumulene, but given the examples in the wikipedia page, I'm going to assume that you are talking about a cumulene that only contains the C=C chain, but nothing crazy like (CO5M=C=C=C=C=C=C=C−(NMe2)2 like I would find in my textbook chapter on metallacumulenes.:)
In that case, there would be one σ bond and one π bond each C=C connection, as a pure double bond could contain one σ and one π bond. There would also be one σ bond for each terminal C−H.If we were to take butatriene as an example also cumulene... then seeing as it is :
H2C=C=C=CH2
... there are three C−C π bonds, three C−C σ bonds, and four C−H σ bonds overall.